GUI and keybindings are saved in the following path (with the non-steam client):
C:\Users\YourUserName\AppData\Local\SWTOR\swtor\settings
Keybindings, iirc, must be saved from the game, otherwise this folder is empty. GUIs do not need to be exported.
If I had to guess, Steam will have an AppData folder path similar where SWTOR items are stowed away. I'll check my wife's files later to confirm, since she runs through Steam.
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As I stated in my comment, I have plenty of room on the drives, though I appreciate your feedback.
Last night, I also tried disabling my anti-virus just to see if that would change anything (though this would be an odd problem, given none of my software or settings have changed, and this is the first time I'm having an issue with a patch). I tried the "compatibility mode" fix that works for other client problems. Nothing has corrected the issue.